Contents

Idea

An ∞\infty-algebra over an (∞,1)(\infty,1)-operad is an ∞-groupoid equipped with higher algebraic operations as encoded by an (∞,1)-operad. Since there is not really any other sensible notion of algebra for an (∞,1)(\infty,1)-operad, we feel free to drop the prefix (although in other cases it can be helpful to disambiguate).